A computational method for reduced-order observers in linear systems

Reduced-order observer design has a long history spanning decades and involving various researchers in the control systems society. The first results on this problem were presented by Luenberger [1]. Thereafter, several papers have been presented examining the problems from different perspectives. One of these approaches is the Sylvester equation approach. This technique aeals mainly with the computational aspects of the problem. In particular, it was Van Dooren who presented some fundamental concepts in this direction using block Hessenberg forms [8]. Later Tsui in [5] presented a parametrization using the aforementioned Sylvester equation. In this paper an alternative algorithm is presented for designing reduced-order observers, which is based on a Diophantine equation. Specifically, the problem of reduced-order observer is studied as a full-order observer problem on a reducedorder subspace using a Diophantine equation. The algorithm uses the Hessenberg form of the pair (C, A). The computation of an output injection is achieved in a computationally efficient way.